Lie Algebroids, Holonomy and Characteristic Classes

Rui Loja Fernandes

Published 2000-07-21, updated 2001-12-11Version 2

We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections, we are able to define holonomy of the orbit foliation of a Lie algebroid and prove a stability theorem. We also introduce secondary or exotic characteristic classes that generalize the modular class of a Lie algebroid.